Naive Set Theory by Paul R. Halmos

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Every mathematician agrees that every mathematician must know some set theory; the disagreement begins in trying to decide how much is some. Originally published in 1960, Naive Set Theory by Prof. Paul R. Halmos is a classic introduction to set theory, which contains his answer to that question.

The purpose of the book is to tell the beginning student of advanced mathematics the basic set-theoretic facts of life, and to do so with the minimum of philosophical discourse and logical formalism. The point of view throughout is that of a prospective mathematician anxious to study groups, or integrals, or manifolds. From this point of view the concepts and methods of this book are merely some of the standard mathematical tools; the expert specialist will find nothing new here.

About the author -- Excerpt from the Wikipedia:

Paul Richard Halmos (1916 - 2006) was a Hungarian-Jewish-born American mathematician who made fundamental advances in the areas of mathematical logic, probability theory, statistics, operator theory, ergodic theory, and functional analysis (in particular, Hilbert spaces). He was also recognized as a great mathematical expositor.